Script to Toggle Fullscreen Area (Blender 2.8)
Solved. What I was looking for was indeed really close to the issue discussed in this post.
Here's the code snippet that does the work:
import bpy

context = bpy.context.copy()

for area in bpy.context.screen.areas:
    if area.type == 'VIEW_3D':
        context['area'] = area
        bpy.ops.screen.screen_full_area(context, use_hide_panels=True)
        bpy.context.space_data.show_gizmo = False
        bpy.context.space_data.overlay.show_overlays = False

Hope it can be of some help to others!